# Reservoir Evaporation Prediction Modeling Based on Artificial Intelligence Methods

^{1}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Problem Statement

#### 1.3. Objectives

## 2. Case Study

_{mean}), minimum (X

_{min}), and maximum (X

_{max}) values for 10 years have been enumerated. Further, the median value for the evaporation data, skewness (Csx), variation coefficient (Cv), and standard deviation (S

_{x}) were calculated for the different time-series data. In terms of the dynamical changes, the relative coefficient of variation was evident for the daily compared with the monthly and weekly time series. Remarkably, the variation between the maximum and minimum values in the daily records reached 7.2 mm/day (i.e., 0.8 − 8 = 7.2), while the difference between the minimum and maximum values for the weekly and monthly time series was 30.5 mm/week and 71 mm/month, respectively. Additionally, Table 1 shows that the low and high skewness indices corresponded to monthly and daily evaporation values, respectively. According to the statistical indicators presented in Table 1, a high fluctuation of evaporation values appeared within the monthly compared with the weekly and daily data.

## 3. Methodology

#### 3.1. RBF-NN Method

#### 3.2. SVR

^{2}are a positive constant, insensitive loss function, and regularization term which denote the Euclidean norm, respectively.

_{a}− y

_{e}||

^{2}is recognized as the squared Euclidean distance between the two feature values.

#### 3.3. Model Structure

#### 3.4. Evaluation Metrics

^{2}) was examined. This indicator is regularly adapted to understand the trend of a model output with the actual values. Secondly, the model was examined by investigating the values of the relative error (RE), which showed the difference between the actual and forecasted values and whether the model over- and/or underestimated the actual values. In addition, RE% represents the maximum error that the model could offer for the model output. The formulas for estimating R

^{2}and RE% are given as

## 4. Result and Discussion

#### 4.1. Results of RBF-NN and SVR Scenario No. 1

_{(t−1)}, E

_{(t−2)}, and E

_{(t−3)}) within the daily timescale.

^{2}= 0.774). Clearly, the agreement between the predicted and actual evaporation rate was significant with the daily timescale. Model III in daily scale has the best accuracy for both methods (RBF-NN and SVR) in all performance criteria. Where the best values of R

^{2}NSE and KGE for SVR are (0.810, 0.781, and 0.795) respectively and for RBF-NN are (0.918, 0.942 and 0.932) respectively. It can be seen that the performance of the predictive model using daily records was superior to weekly and monthly records. Additionally, the accuracy of the results within the monthly timescale was better than weekly. This indicates that increasing the timescale may or may not improve the accuracy of the predictive model. Hence, inspecting the performance of the suggested models under several timescales is crucial.

#### 4.2. Results of RBF-NN and SVR Scenario No. 2

^{2}. This shows that the input combinations (E

_{(t−1)}, E

_{(t−2)}, T

_{(t−1)}, T

_{(t−2)}) enhanced the performance of the predictive model. As seen in Table 5, using weekly and monthly data provided poor predictions. Therefore, it is pertinent to consider the influence of the timescale on the accuracy of results. On the other hand, the RBF-NN outperformed the SVR technique, according to the four indices (RMSE = 0.281 mm/day; MAE = 0.0201 mm/day; RE% = +11, −12; and R

^{2}= 0.95). Model II in daily scale has the best accuracy for both methods (RBF-NN and SVR) where the best values of R

^{2}NSE and KGE for SVR are (0.887, 0.912, and 0.892) respectively and for RBF-NN are (0.951, 0.968 and 0.935) respectively.

#### 4.3. Comparison of the Models

_{max}value of 19.5%. In fifth place was the SVR method considering two input variables, daily data, and under the second scenario. The SVR and RBF-NN methods were in sixth and seventh place when applying the SVR with Model III and RBF-NN with Model II under the first scenario with daily data, for which the magnitude of the relative error was 20.2% and 20.8%, respectively. It could be observable that the daily records are more suitable for the prediction models to attain accurate results. It seems that the prediction of the evaporation using small time scale (i.e., daily) is more understandable for the RBF-NN and SVR. The RBF-NN model was efficient even with minimum input variable. This indicates that the RBF-NN model could be better in case add some modifications for its procedure.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AHD | Aswan High Dam |

AI | Artificial Intelligence |

ANFIS | Adaptive Neuro-Fuzzy Inference System |

ANN | Artificial Neural Networks |

DID | Department of Irrigation and Drainage |

ELM | Extreme Learning Machine |

FFNN | Feedforward Neural Networks |

GRNN | Generalized Regression Neural Networks |

LS-SVM | Least Square Support Vector Machines |

MAE | Mean Absolute Error |

MLP-NN | Multilayer Perceptron Neural Network |

MSE | Mean Square Error |

PE | Pan Evaporation |

RBF-NN | Radial Basis Function Neural Network |

RB | Radial Basis |

RE | Relative Error |

RMSE | Root Mean Square Error |

SVR | Support Vector Regression |

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**Figure 3.**Autocorrelation functions of the evaporation series (

**a**) for daily data (

**b**) for weekly data (

**c**) for monthly data.

**Figure 4.**The distribution of the predicted evaporation data by SVM method for the first scenario. (

**a**) predicted pattern versus actual data within daily (

**c**) weekly records, (

**e**) monthly; (

**b**) scatterplot for the evaporation data within daily time scale, (

**d**) weekly, (

**f**) monthly data.

**Figure 5.**The distribution of the predicted evaporation data by (RBF-NN) method for the first scenario. (

**a**) predicted pattern versus actual data within daily (

**c**) weekly records, (

**e**) monthly; (

**b**) scatterplot for the evaporation data within daily time scale, (

**d**) weekly, (

**f**) monthly data.

**Figure 6.**The distribution of the predicted evaporation data by SVM method for the second scenario. (

**a**) predicted pattern versus actual data within daily (

**c**) weekly records, (

**e**) monthly; (

**b**) scatterplot for the evaporation data within daily time scale, (

**d**) weekly, (

**f**) monthly data.

**Figure 7.**The distribution of the predicted evaporation data by ANN (RBF-NN) method for the second scenario. (

**a**) predicted pattern versus actual data within daily (

**c**) weekly records, (

**e**) monthly; (

**b**) scatterplot for the evaporation data within daily time scale, (

**d**) weekly, (

**c**) monthly data).

Time Scale | X_{mean} | S_{x} | Cv (S_{x}/X_{mean}) | Csx | X_{max} | X_{min} | Median |
---|---|---|---|---|---|---|---|

Daily | 3.361 | 1.215 | 0.361 | 0.431 | 8 | 0.8 | 3 |

Weekly | 23.527 | 5.02 | 0.213 | 0.396 | 41.9 | 11.4 | 22.85 |

Monthly | 100.637 | 13.386 | 0.133 | 0.119 | 137.7 | 66.7 | 99.85 |

_{mean}= mean value; S

_{x}= standard deviation; Cv = coefficient of variation; Csx = skewness; X

_{min}= minimum value and X

_{max}= maximum value.

Model | Input Combination | Output |
---|---|---|

Model I | E_{(t−1)} | E(t) |

Model II | E_{(t−1)}, E_{(t−2)} | E(t) |

Model III | E_{(t−1)}, E_{(t−2)}, E_{(t−3)} | E(t) |

Model IV | E_{(t−1)}, E_{(t−2)}, E_{(t−3)}, E_{(t−4)} | E(t) |

Model V | E_{(t−1)}, E_{(t−2)}, E_{(t−3)}, E_{(t−4)}, E_{(t−5)} | E(t) |

Model | Input Combination | Output |
---|---|---|

Model I | E_{(t−1)}, T_{(t−1)} | E(t) |

Model II | E_{(t−1)}, E_{(t−2)}, T_{(t−1)}, T_{(t−2)} | E(t) |

Model III | E_{(t−1)}, E_{(t−2)}, E_{(t−3)}, T_{(t−1)}, T_{(t−2)}, T_{(t−3)} | E(t) |

Model IV | E_{(t−1)}, E_{(t−2)}, E_{(t−3)}, E_{(t−4)}, T_{(t−1)}, T_{(t−2)}, T_{(t−3)}, T_{(t−4)} | E(t) |

Model V | E_{(t−1)}, E_{(t−2)}, E_{(t−3)}, E_{(t−4)}, E_{(t−5)}, T_{(t−1)}, T_{(t−2)}, T_{(t−3)}, T_{(t−4)}, T_{(t−5)} | E(t) |

**Table 4.**The performance criteria (RMSE, MAE, R

^{2}and RE %) values for Scenario No. 1 using RBF-NN and SVR methods.

Time Increment | Input Models | SVR | RBF-NN | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | R^{2} | RE % | NSE | KGE | RMSE | MAE | R^{2} | RE % | NSE | KGE | ||

Daily | Model I | 0.690 | 0.099 | 0.802 | +21.2, −26 | 0.742 | 0.765 | 0.432 | 0.022 | 0.875 | +19.6, −18.3 | 0.852 | 0.812 |

Model II | 0.808 | 0.060 | 0.802 | +22.8, −21.4 | 0.753 | 0.771 | 0.820 | 0.042 | 0.872 | +20.8, −20.3 | 0.883 | 0.857 | |

Model III | 0.516 | 0.042 | 0.810 | +20.2, −19.8 | 0.781 | 0.795 | 0.318 | 0.021 | 0.918 | +18, −18.5 | 0.942 | 0.932 | |

Model IV | 2.210 | 0.115 | 0.675 | +23.7, −26.4 | 0.642 | 0.654 | 2.110 | 0.110 | 0.781 | +22, −25.4 | 0.803 | 0.798 | |

Weekly | Model I | 1.043 | 0.102 | 0.342 | +39.5, −39.2 | 0.428 | 0.453 | 1.845 | 0.180 | 0.775 | +38.4, −36.2 | 0.781 | 0.732 |

Model II | 2.057 | 0.202 | 0.338 | +37.4, −36.2 | 0.365 | 0.314 | 2.409 | 0.236 | 0.768 | +36.8, −35.3 | 0.758 | 0.748 | |

Model III | 1.561 | 0.153 | 0.340 | +37, −36.8 | 0.337 | 0.327 | 3.101 | 0.305 | 0.730 | +36.6, −34.8 | 0.742 | 0.763 | |

Model IV | 0.887 | 0.086 | 0.347 | +35.3, −33.6 | 0.382 | 0.358 | 0.734 | 0.072 | 0.774 | +34, −32.5 | 0.802 | 0.772 | |

Model V | 0.944 | 0.093 | 0.386 | +37.8, −38.7 | 0.412 | 0.402 | 4.217 | 0.415 | 0.794 | +36.4, −38.2 | 0.787 | 0.754 | |

Monthly | Model I | 8.931 | 1.823 | 0.410 | +36.4, −35.3 | 0.483 | 0.437 | 4.887 | 0.997 | 0.664 | +33.4, −31.3 | 0.631 | 0.657 |

Model II | 3.675 | 0.750 | 0.503 | +30.5, −29.7 | 0.521 | 0.537 | 1.340 | 0.279 | 0.816 | 28.7, −27.3 | 0.824 | 0.784 | |

Model III | 10.719 | 2.235 | 0.468 | +33, −34.5 | 0.483 | 0.438 | 1.497 | 0.305 | 0.783 | +32.3, −31.2 | 0.795 | 0.762 |

^{2})correlation coefficient; (NSE) Nash-Sutcliffe efficiency and (KGE’) modified Kling-Gupta efficiency.

**Table 5.**The performance criteria (RMSE, MAE, R

^{2}and RE %) values for Scenario No. 2 using RBF-NN and SVR methods.

Time Increment | Input Models | SVR | RBF-NN | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | R^{2} | RE % | NSE | KGE | RMSE | MAE | R^{2} | RE % | NSE | KGE | ||

Daily | Model I | 0.955 | 0.087 | 0.897 | +20, −25 | 0.872 | 0.863 | 0.542 | 0.044 | 0.904 | +19.5, −18.3 | 0.913 | 0.884 |

Model II | 0.421 | 0.032 | 0.887 | +18, −20 | 0.912 | 0.891 | 0.281 | 0.020 | 0.951 | +11, −12 | 0.968 | 0.935 | |

Model III | 1.011 | 0.088 | 0.884 | +23.4, −27.8 | 0.901 | 0.854 | 0.925 | 0.092 | 0.879 | +20.3, −22.7 | 0.842 | 0.852 | |

Model IV | 1.235 | 1.074 | 0.812 | +46, −45 | 0.783 | 0.827 | 1.078 | 0.947 | 0.851 | +41, −42.4 | 0.793 | 0.835 | |

Model V | 1.864 | 1.942 | 0.721 | +57, −46.5 | 0.757 | 0.743 | 1.143 | 1.048 | 0.774 | +40.5, −43 | 0.736 | 0.783 | |

Weekly | Model I | 1.204 | 0.121 | 0.501 | +26.8, −29.4 | 0.482 | 0.527 | 0.754 | 0.068 | 0.878 | +25.7, −26.2 | 0.821 | 0.858 |

Model II | 1.002 | 0.085 | 0.513 | +25.4, −28 | 0.537 | 0.548 | 0.662 | 0.061 | 0.880 | +24.8, −25.3 | 0.902 | 0.885 | |

Model III | 0.656 | 0.042 | 0.523 | +25, −26.3 | 0.541 | 0.572 | 0.524 | 0.045 | 0.867 | +24.6, −23.8 | 0.927 | 0.908 | |

Model IV | 0.695 | 0.048 | 0.516 | +29.4, −31.2 | 0.537 | 0.493 | 0.711 | 0.067 | 0.872 | +28.7, −29.8 | 0.828 | 0.853 | |

Model V | 1.924 | 2.073 | 0.483 | +61, −68.6 | 0.492 | 0.524 | 1.177 | 1.069 | 0.845 | +43.8, −42.5 | 0.781 | 0.812 | |

Monthly | Model I | 5.231 | 0.952 | 0.643 | +26.6, −24 | 0.674 | 0.628 | 4.328 | 0.985 | 0.452 | +26.5, −23.5 | 0.402 | 0.483 |

Model II | 2.821 | 0.857 | 0.657 | +27.9, −22.3 | 0.648 | 0.673 | 2.325 | 0.721 | 0.523 | +24.2, −23.2 | 0.498 | 0.557 | |

Model III | 1.354 | 0.424 | 0.778 | +22, −22 | 0.793 | 0.804 | 1.112 | 0.241 | 0.871 | +21.3, −19.8 | 0.907 | 0.892 | |

Model IV | 2.823 | 0.925 | 0.703 | +23, −24 | 0.685 | 0.712 | 1.334 | 0.295 | 0.584 | +25.6, −24.5 | 0.518 | 0.547 | |

Model V | 3.258 | 1.892 | 0.521 | +51, −63.2 | 0.547 | 0.572 | 2.871 | 1.328 | 0.542 | +43.5, −58.3 | 0.487 | 0.538 |

Rank | Method | No. of Model | Scale Time | No. of Scenario |
---|---|---|---|---|

1 | RBF-NN | Model II | Daily | 2 |

2 | RBF-NN | Model III | Daily | 1 |

3 | RBF-NN | Model I | Daily | 2 |

4 | RBF-NN | Model I | Daily | 1 |

5 | SVR | Model II | Daily | 2 |

6 | SVR | Model III | Daily | 1 |

7 | RBF-NN | Model II | Daily | 1 |

8 | RBF-NN | Model III | Monthly | 2 |

9 | SVR | Model III | Monthly | 2 |

10 | RBF-NN | Model III | Daily | 2 |

11 | SVR | Model II | Daily | 1 |

12 | SVR | Model IV | Monthly | 2 |

13 | RBF-NN | Model II | Monthly | 2 |

14 | RBF-NN | Model III | Weekly | 2 |

15 | RBF-NN | Model II | Weekly | 2 |

16 | SVR | Model I | Daily | 2 |

17 | RBF-NN | Model IV | Daily | 1 |

18 | RBF-NN | Model IV | Monthly | 2 |

19 | SVR | Model I | Daily | 1 |

20 | RBF-NN | Model I | Weekly | 2 |

21 | SVR | Model III | Weekly | 2 |

22 | SVR | Model IV | Weekly | 1 |

23 | RBF-NN | Model I | Monthly | 2 |

24 | SVR | Model I | Monthly | 2 |

25 | SVR | Model III | Daily | 2 |

26 | SVR | Model II | Monthly | 2 |

27 | SVR | Model II | Weekly | 2 |

28 | RBF-NN | Model II | Monthly | 1 |

29 | SVR | Model I | Weekly | 2 |

30 | RBF-NN | Model IV | Weekly | 2 |

31 | SVR | Model II | Monthly | 1 |

32 | SVR | Model IV | Weekly | 2 |

33 | RBF-NN | Model III | Monthly | 1 |

34 | RBF-NN | Model I | Monthly | 1 |

35 | RBF-NN | Model IV | Weekly | 1 |

36 | SVR | Model III | Monthly | 1 |

37 | SVR | Model IV | Weekly | 1 |

38 | SVR | Model I | Monthly | 1 |

39 | RBF-NN | Model III | Weekly | 1 |

40 | RBF-NN | Model II | Weekly | 1 |

41 | SVR | Model III | Weekly | 1 |

42 | SVR | Model II | Weekly | 1 |

43 | RBF-NN | Model V | Weekly | 1 |

44 | RBF-NN | Model I | Weekly | 1 |

45 | SVR | Model V | Weekly | 1 |

46 | SVR | Model I | Weekly | 1 |

47 | RBF-NN | Model IV | Daily | 2 |

48 | RBF-NN | Model V | Daily | 2 |

49 | RBF-NN | Model V | Weekly | 2 |

50 | SVR | Model IV | Daily | 2 |

51 | SVR | Model V | Daily | 2 |

52 | SVR | Model V | Weekly | 2 |

53 | RBF-NN | Model V | Monthly | 2 |

54 | SVR | Model V | Monthly | 2 |

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## Share and Cite

**MDPI and ACS Style**

Allawi, M.F.; Binti Othman, F.; Afan, H.A.; Ahmed, A.N.; Hossain, M.S.; Fai, C.M.; El-Shafie, A.
Reservoir Evaporation Prediction Modeling Based on Artificial Intelligence Methods. *Water* **2019**, *11*, 1226.
https://doi.org/10.3390/w11061226

**AMA Style**

Allawi MF, Binti Othman F, Afan HA, Ahmed AN, Hossain MS, Fai CM, El-Shafie A.
Reservoir Evaporation Prediction Modeling Based on Artificial Intelligence Methods. *Water*. 2019; 11(6):1226.
https://doi.org/10.3390/w11061226

**Chicago/Turabian Style**

Allawi, Mohammed Falah, Faridah Binti Othman, Haitham Abdulmohsin Afan, Ali Najah Ahmed, Md. Shabbir Hossain, Chow Ming Fai, and Ahmed El-Shafie.
2019. "Reservoir Evaporation Prediction Modeling Based on Artificial Intelligence Methods" *Water* 11, no. 6: 1226.
https://doi.org/10.3390/w11061226